4. Asymmetric eclipse curve of SY Mus
It is important to note that our time of mid-eclipse is not based on the light curve shape but on RV measurements. This is a crucial point because we intend to study asymmetries in the eclipse curve.
4.1. Column density of neutral hydrogen
During ingress and egress we observe attenuation at wavelengths due to Rayleigh scattering and a second opacity source of up to now unknown origin. This second source of opacity has already been described in Pereira et al. (1995).
In Fig. 3, we show the continuum variation at and . At 1325 Å Rayleigh scattering efficiency is very high, getting smaller towards longer wavelengths. The eclipse curve is clearly asymmetric with respect to the phase of central eclipse. At ingress a sharp flux reduction starts at . The reappearance of the hot continuum is less steep and continues until approximately .
We determine the column densities of neutral hydrogen, , with a similar approach as the one adopted by Pereira et al. (1995). We rewrite their Eq. 3
The term models an additional opacity source in a wavelength independent way, as the IUE low resolution spectra do not allow a more detailed approach. We use the spectrum SWP56762 observed at as reference spectrum . This spectrum does not yet show attenuation due to Rayleigh scattering. In addition it is least affected by nebular emission, as it is taken close to the onset of the eclipse.
By fitting the ingress and egress variation with Eq. 2, we derive the column densities and additional optical depths (Table 5). The error in the derived column density of neutral hydrogen is estimated to be of the order of . At low and high column densities the uncertainties tend to be even larger. This error does not include systematic effects due to line blanketing discussed in Sect. 5. For those IUE spectra we have in common with Pereira et al. (1999), we find agreement within the error bars. In Fig. 4 the column densities are plotted as a function of the impact parameter b, given by
Table 5. Column density of neutral hydrogen and the optical depth in SY Mus according to Eq. 2 as a function of orbital phase , and impact parameter b (in units of M-giant radii). The errors of are of the order of 50%..
Fig. 4 shows that the column density of neutral hydrogen in SY Mus is clearly asymmetric with respect to mid-eclipse.
Because the density distribution around SY Mus is not symmetric, we model the ingress and egress column densities separately with two independent, semi-spherically symmetric solutions for the volume density
where is the mass-loss rate of the M-giant, and the velocity in units of the terminal velocity . For a neutral wind which consists mainly of hydrogen, the mean atomic weight is . The total column density of hydrogen along the line of sight l is then given by
where b and r are in units of the M-giant radius . The parameter a is defined by
We want to solve Eq. 5 for the velocity law . According to Knill et al. (1993), it is particularly advantageous to expand the function into a Taylor series
as the velocity law, , is then given by
with the constants recursively defined by
Due to the limited orbital coverage and limited precision of the column densities, a unique determination of the velocity profile is not possible. Therefore, we reduce Eq. 7 to the first term () and one term of order . Thus we rewrite Eq. 7 into
and Eq. 8 reduces to
The factors , , and the exponent k in Eq. 11 are our fit parameters.
Eq. 10 requires that we know the total column density of hydrogen as a function of impact parameter b. In symbiotic binaries a fraction of the wind is ionized by the hot star. Thus the measured column densities of neutral hydrogen can be substantially smaller than the total column density of hydrogen.
During egress of SY Mus, there is a region around where (see Fig. 5). From to , there is a sudden drop in the column density of neutral hydrogen (see Fig. 5). In the following we model this behaviour by a wind that has reached terminal velocity at , with , and is substantially ionized at impact parameters . From the sudden decrease in column density we also deduce that the transition from mainly neutral to mainly ionized hydrogen is almost instantaneous. Thus, the amount of ionized material at is negligible, and our measured column density of neutral hydrogen at is close to the total column density of hydrogen .
The first term in Eq. 10 and Eq. 11 is the dominant term for large b values, and corresponds to the solution of a stellar wind with constant expansion velocity , where the volume density is proportional to . A total column density of hydrogen of at , where the first term in Eq. 10 dominates, leads to
Typical terminal velocities for M-giant winds from molecular absorption band analysis are in the range . In the following we adopt This implies a mass-loss rate for the M-giant in SY Mus of
The second term in Eq. 10 and Eq. 11 is the dominant term for small impact parameters. It determines where the acceleration of the M-giant wind takes place. The best fit parameters for the second term in Eq. 10 are and (see Fig. 5). The resulting velocity profile is shown in Fig. 6.
If we assume, that for column densities , ionization becomes significant, the ingress data does not allow to derive a mass-loss rate (see Fig. 4). Assuming the mass-loss rate derived from the egress data, we find and , with large uncertainties. The wind acceleration then takes place at (see Fig. 6).
© European Southern Observatory (ESO) 1999
Online publication: August 25, 1999